Question

Longly Trucking is issuing a 20-year bond with a $2,000 face value tomorrow. The issue is to pay an 8% coupon rate, because that was the interest rate while it was being planned. However, rates have increased suddenly and are expected to be 9.2% when the bond is marketed. What will Longly receive for each bond tomorrow? Assume bond coupons are paid semiannually. Round PVFA and PVF values in intermediate calculations to four decimal places. Do not round other intermediate calculations. Round the answer to the nearest cent.

Answer 1

Answer:

Face value of Bond = $2,000

Coupon rate = 8%

Bond coupons are paid semiannually

Semiannual coupon = $2,000 * 8%/2 = $80

Time to maturity = 20 year = 40 semiannual periods

Market rate of interest (semiannual) = 9.2%/2 = 4.6%

PVFA = = [1 - 1/(1 + k) ⁿ] / k = (1 - 1/(1 + 4.6%) ⁴⁰) / 4.6% = 18.1418

PVF = = 1 / (1 + k) ⁿ = 1 / (1 + 4.6%) ⁴⁰ = 0.1655

Value of the bond = Semiannual coupon * PVFA + Face value at redemption * PVF

= 80 * 18.1418 +2000 * 0.1655

= $1,782.34

Value of the bond = $1,782.34